What is the Greatest Common Factor of 77208 and 77216?

Greatest common factor (GCF) of 77208 and 77216 is 8.

GCF(77208,77216) = 8

We will now calculate the prime factors of 77208 and 77216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77208 and 77216.

How to find the GCF of 77208 and 77216?

We will first find the prime factorization of 77208 and 77216. After we will calculate the factors of 77208 and 77216 and find the biggest common factor number .

Step-1: Prime Factorization of 77208

Prime factors of 77208 are 2, 3, 3217. Prime factorization of 77208 in exponential form is:

77208 = 2³ × 3¹ × 3217¹

Step-2: Prime Factorization of 77216

Prime factors of 77216 are 2, 19, 127. Prime factorization of 77216 in exponential form is:

77216 = 2⁵ × 19¹ × 127¹

Step-3: Factors of 77208

List of positive integer factors of 77208 that divides 77208 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 3217, 6434, 9651, 12868, 19302, 25736, 38604

Step-4: Factors of 77216

List of positive integer factors of 77216 that divides 77208 without a remainder.

1, 2, 4, 8, 16, 19, 32, 38, 76, 127, 152, 254, 304, 508, 608, 1016, 2032, 2413, 4064, 4826, 9652, 19304, 38608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77208 and 77216. The biggest common factor number is the GCF number.
So the greatest common factor 77208 and 77216 is 8.

Also check out the Least Common Multiple of 77208 and 77216